crows, buzzards and rabbits

[ruralcheshire]

Hi, until few years ago we had no problem with rabbits, but now a colony of crows is been living in the woods and as a results they scare off the buzzards who in turn were keeping the rabbit population under check.
Now the rabbit run riot all our vegetables are been eaten, the garden is full of holes and there is only one pair of buzzards left.
I saw 6 crows chasing a buzzard in flight.
we even had to build extra defence for the bird food because they were stealing it, leaving all our birds (woodpeckers, tits, robins, wood pidgeon blackbirs etc) without food. On top of it they are astonishingly noisy in the morning.
Town people please refrain from replying, we are living in a farm miles away from the closest village and we don't want to use drastic measure.
anybody gor any idea on how to get rid of this birds?